Analytical expressions for dead time Effects for Various Practical cases

The problem of the eect of the dead time on the detection statistics has been treated in previous work in a general framework, using the methods of renewal theory [1]. The theory was developed to cover both non-paralysing and paralysing dead times, in the former case both withxed and random dead time, and the cases of triggered and arbitrary measurement start times. Some concrete examples with explicit expressions for the mean and the variance were given in [1] and [2]. The objective of this paper is to give concrete formulae for the mean, variance, and sometimes for the whole probability distribution, for several cases of practical interest. The results are expected to be useful both in evaluating measurements as well as for benchmarking Monte-Carlo methods, used for empirical corrections for dead time eects.